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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A nonsmooth nonconvex optimization algorithm for two-stage optimization problems

An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties such as prox-regularity assumed in many nonsmooth nonconvex optimization algorithms, (2) the objective can not be analytically expressed and (3) the evaluation of function values and subgradients are computationally expensive. To address these challenges, this report first examines the properties that exist in many two-stage problems, specifically upper-C 2 objectives. Then, we show that quadratic penalty method for securityconstrained alternating current optimal power flow (SCACOPF) contingency problems can make the contingency solution functions upper-C 2 . Based on these observations, a simplified bundle algorithm that bears similarity to sequential quadratic programming (SQP) method is proposed. It is more efficient in implementation and computation compared to conventional bundle methods. Global convergence analysis of the algorithm is presented under novel and reasonable assumptions. The proposed algorithm therefore fills the gap of theoretical convergence for smoothed SCACOPF problems. The inconsistency that might arise in our treatment of the constraints are addressed through a penalty algorithm whose convergence analysis is also provided. Finally, theoretical capabilities and numerical performance of the algorithm are demonstrated through numerical examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Numerical modeling of D-mappings with applications to chemical kinetics

Numerical modeling of D-mappings was studied and applied to solving nonlinear stiff systems. These mappings were locally linearized for convergence analysis, and some applications were made to chemical kinetics. The technique avoids using multistep implicit codes that require inversion of Jacobian matrices, but depends on the Jacobians for its convergence analysis.

Dey, S. K.↗
DOE OSTI2021

Examination of probability distribution of mixture fraction in LES/FDF modelling of a turbulent partially premixed jet flame

An accurate prediction of the probability density function (PDF) of the mixture fraction is crucial to the prediction of combustion since mixing plays an important role in turbulent non-premixed and partially premixed flames. This work provides an assessment of the large-eddy simulation (LES)/filtered density function (FDF) method for the prediction of the PDF of the mixture fraction. The advantage of the LES/FDF method is that it provides the full predictions of the statistical distribution of scalars including the mixture fraction. The predictive accuracy of the method for the PDF is yet to be fully validated. Assessing the prediction of the PDF of the mixture fraction, a conserved scalar, is an important starting point. The Sydney/Sandia inhomogeneous inlet jet flame is used as a test case. A quick comparison shows that the LES/FDF predicted PDF shapes of the mixture fraction deviate significantly from the commonly presumed Beta-PDF as well as from the experimental data in the flame. Here, to examine the source of the discrepancy, we clarify the different PDF definitions used in the comparison among the predictions, measurements, and the presumed shape PDFs. The discrepancy observed from the comparison is largely reconciled by clarifying the difference between the PDFs that are examined. The PDF of the resolved mixture fraction is shown to be close to the Beta-PDF in both the measurements and predictions, while the PDF directly deduced from the LES/FDF particles deviates significantly from the Beta-PDF. A multimodal PDF analysis and a pseudo convergence analysis are conducted to provide plausible evidence to support the predicted multimodal PDF shapes. The sub-filter scale FDF is shown to be close to the Beta-PDF too through the construction of a synthesized PDF, which supports the common presumed Beta-PDF assumption used in the presumed PDF methods when combined with LES.

42 ENGINEERING↗
NASA NTRS1979

Convergent perturbation analysis of intense coherent multiphoton interactions

Use has been made of flow graphs to deduce Feenberg perturbation expansions for radiative interactions. It is demonstrated that these expansions can in certain cases be summed to provide closed form expressions for the molecular response. In particular, it is shown that the coherent state response can be obtained by the summation of a continued fraction perturbation expansion for the harmonic oscillator. Anharmonicity in the lower levels is treated and its shown to introduce Rabi flopping identifiable with multiphoton transitions among isolated tightly coupled subsystems of levels. Relevance to laser induced multiphoton excitation and energy level shift calculations in the presence of a strong field are also discussed.

Gower, M. C.↗
NASA NTRS1991

Analysis and convergence of the MAC scheme. Part 1: The linear problem

The MAC discretization of fluid flow is analyzed for the stationary Stokes equations. It is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations. Estimates using mesh dependent norms analogous to the standard H(sup 1) and L(sup 2) norms are given for the velocity and pressure, respectively.

Nicolaides, R. A.↗
DOE OSTI2025

Conditional Pseudo-Reversible Normalizing Flow for Surrogate Modeling in Quantifying Uncertainty Propagation

We introduce a conditional pseudo-reversible normalizing flow (PR-NF) that directly learns conditional probability distributions from noisy physical models to efficiently quantify both forward and inverse uncertainty propagation. Traditional surrogate modeling approaches approximate only the deterministic component of physical models, requiring separate noise characterization and computationally expensive sampling methods for inverse problems. Here, in this work, we develop the conditional PR-NF model to directly learn and efficiently generate samples from the conditional probability density functions (PDFs). The training process utilizes dataset consisting of input-output pairs without requiring prior knowledge about the noise and the function. Once trained, our model efficiently generates samples from conditional PDFs for any input within the training domain. Moreover, the pseudo-reversibility feature allows for the use of fully connected neural network architectures, which simplifies the implementation and enables theoretical analysis. We provide a rigorous convergence analysis of the conditional PR-NF model, showing its ability to converge to the target conditional PDF using the Kullback−Leibler divergence. To demonstrate the effectiveness of our method, we apply it to several benchmark tests and a real-world geologic carbon storage problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multirate Exponential Rosenbrock Methods

In this paper we propose a novel class of methods for high-order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the action of matrix φ functions within explicit exponential Rosenbrock (ExpRB) methods, thereby called multirate ExpRB (MERB) methods. They consist of the solution to a sequence of modified “fast” initial-value problems, which may themselves be approximated through subcycling any desired initial-value problem solver. In addition to proving how to construct MERB methods from certain classes of ExpRB methods, we provide rigorous convergence analysis of these methods and derive efficient MERB schemes of orders 2 through 6 (the highest-order infinitesimal multirate methods to date). Lastly, we then present numerical simulations to confirm these theoretical convergence rates and to compare the efficiency of MERB methods against other recently introduced high-order multirate methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Assessing convergence in global sensitivity analysis: a review of methods for assessing and monitoring convergence

In global sensitivity analysis (GSA) of a model, a proper convergence analysis of metrics is essential for ensuring a level of confidence or trustworthiness in sensitivity results obtained, yet is somewhat deficient in practice. The level of confidence in sensitivity measures, particularly in relation to their influence and support for decisions from scientific, social and policy perspectives, is heavily reliant on the convergence of GSA. We review the literature and summarize the available methods for monitoring and assessing convergence of sensitivity measures based on application purposes. The aim is to expose the various choices for convergence assessment and encourage further testing of available methods to clarify their level of robustness. Furthermore, the review identifies a pressing need for comparative studies on convergence assessment methods to establish a clear hierarchy of effectiveness and encourages the adoption of systematic approaches for enhanced robustness in sensitivity analysis.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Analysis of the SiMPL Method for Density-Based Topology Optimization

We present a rigorous convergence analysis of a new method for density-based topology optimization that provides pointwise bound-preserving design updates and faster convergence than other popular first-order topology optimization methods. Due to its strong bound preservation, the method is exceptionally robust, as demonstrated in numerous examples here and in the companion article [D. Kim et al., Struct. Multidiscip. Optim., 68 (2025), 74]. Furthermore, it is easy to implement with clear structure and analytical expressions for the updates. Our analysis covers two versions of the method, characterized by the employed line search strategies. We consider a modified Armijo backtracking line search and a Bregman backtracking line search. For both line search algorithms, our algorithm delivers a strict monotone decrease in the objective function and further intuitive convergence properties, e.g., strong and pointwise convergence of the density variables on the active sets, norm convergence to zero of the increments, convergence of the Lagrange multipliers, and more. In addition, the numerical experiments demonstrate apparent mesh-independent convergence of the algorithm. Here, we refer to the new algorithm as the SiMPL method (pronounced “simple”), which stands for Sigmoidal Mirror descent with a Projected Latent variable.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Acceleration of convergence of vector sequences

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

Sidi, A.↗
NASA NTRS1986

Acceleration of convergence of vector sequences

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iterative. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

Sidi, A.↗
NASA NTRS1999

Approximation of the Newton Step by a Defect Correction Process

In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into the system. This operator is motivated by local mode analysis. The operator can be used also for preconditioning in Generalized Minimum Residual (GMRES). We give a detailed convergence analysis for the defect correction process and show the derivation of the modifying operator. Numerical tests are done on the small disturbance shape optimization problem in two dimensions for the defect correction process and for GMRES.

Arian, E.↗
DOE OSTI2024

The eXtended virtual element method for elliptic problems with weakly singular solutions

This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The X-VEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to handle highly generic enrichment functions, including singularities arising from fractured domains. By achieving consistency on the enrichment space, the method is proven to achieve arbitrary approximation orders even in the presence of singular solutions. The paper includes a complete convergence analysis under general assumptions on mesh regularity, and numerical experiments validating the method’s accuracy on various mesh families, demonstrating optimal convergence rates in the L 2 - and H 1 - norms on fractured or L-shaped domains.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Averaging analysis for discrete time and sampled data adaptive systems

Earlier continuous time averaging theorems are extended to the nonlinear discrete time case. Theorems for the study of the convergence analysis of discrete time adaptive identification and control systems are used. Instability theorems are also derived and used for the study of robust stability and instability of adaptive control schemes applied to sampled data systems. As a by product, the effects of sampling on unmodeled dynamics in continuous time systems are also studied.

Fu, Li-Chen↗
NASA NTRS1989

Integrated structural analysis and design using 3-D finite elements

The optimum design of the shape of a hole in a plate in tension is obtained with a design algorithm based on partially converged analysis. The plate is modeled by three-dimensional finite elements, and an EBE PCG iterative solution algorithm is used for solving the equations of equilibrium. Several parametrizations of the optimum shape are considered, and it is found that a sine series can describe the optimum shape with only three design variables. The optimum shape compares well with an experimental optimum obtained by Durelli.

Barthelemy, B.↗
NASA NTRS1994

On the convergence of local approximations to pseudodifferential operators with applications

We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.

Hagstrom, Thomas↗